To improve the robustness of NMF approaches for demixing functional data, we make use of the growing literature on “guaranteed NMF” approaches — methods for computing a non-negative matrix factorization that are guaranteed to output the “correct” answer under suitable conditions and assumptions [1]}, [2]}, [3]}, [4]}. In practice, these methods work well on clean data of sufficiently small dimensionality, but are not robust to noise and scale poorly to high-dimensional data. We can solve both of these issues by “superpixelizing" the denoised version of \(\mathbf {Y}\) ; the resulting NMF initialization method improves significantly on state of the art methods for processing dendritic and axonal data. We also take advantage of the sparse, low-rank structure of \(\mathbf {U}\)  and \(\mathbf {V}\)  to speed up the NMF iterations.
